Extraction of the intercellular skeleton from 2D images of embryogenesis using eikonal equation and advective subjective surface method

Paul Bourgine; Peter Frolkovic; Karol Mikula; Nadine Peyrieras; Mariana Remesikova

hal-00723370, version 1

Extraction of the intercellular skeleton from 2D images of embryogenesis using eikonal equation and advective subjective surface method

Paul Bourgine ^1, 2, Peter Frolkovic ³, Karol Mikula ³, Nadine Peyrieras ^4, 5, 6, Mariana Remesikova ³

Scale Space and Variational Methods in Computer Vision Springer Verlag (Ed.) (2009) 38-49

Abstract: We suggest an efficient method for automatic detection of the intercellular skeleton in microscope images of early embryogenesis. The method is based on the solution of two advective PDEs. First, we solve numerically the time relaxed eikonal equation in order to obtain the signed distance function to a given set - a set of points representing cell centers or a set of closed curves representing segmented inner borders of cells. The second step is a segmentation process driven by the advective version of subjective surface equation where the velocity field is given by the gradient of the computed distance function. The first equation is discretized by Rouy-Tourin scheme and we suggest a fixing strategy that significantly improves the speed of the computation. The second equation is solved using a classical upwind strategy. We present several test examples and we show a practical application - the intercellular.

1: Centre de recherche en épistémologie appliquée (CREA)
CNRS : UMR7656 – Polytechnique - X
2: Réseau National des Systèmes Complexes (RNSC)
CNRS : UMR0 – INSERM : U0 – Institut national de la recherche agronomique (INRA) : UMR0 – Institut Français de Recherche pour l'Exploitation de la Mer (IFREMER) – Centre de coopération internationale en recherche agronomique pour le développement [CIRAD] : UMR0 – INRIA – Institut de recherche pour le développement [IRD] – CGE – CPU
3: Department of Mathematics (STUBA)
Slovak University of Technology
4: Neurobiologie et Développement (N&eD)
CNRS : UPR3294 – Université Paris XI - Paris Sud
5: Institut des Systèmes Complexes - Paris Ile-de-France (ISC-PIF)
CNRS : UMR7656 – Institut Curie – Université Paris XI - Paris Sud – Université Paris I - Panthéon-Sorbonne – Université Pierre et Marie Curie [UPMC] - Paris VI – École normale supérieure de Cachan - ENS Cachan – Ecole normale supérieure de Paris - ENS Paris – Polytechnique - X
6: Institut de Neurobiologie Alfred Fessard (INAF)
CNRS : FRC2118

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From: Alain Perignon <>
Submitted on: Thursday, 9 August 2012 13:20:49
Updated on: Thursday, 9 August 2012 13:20:49

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DOI: 10.1007/978-3-642-02256-2_4

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%% hal-00723370, version 1
%% http://hal.archives-ouvertes.fr/hal-00723370
@incollection{bourgine:hal-00723370,
    hal_id = {hal-00723370},
    url = {http://hal.archives-ouvertes.fr/hal-00723370},
    title = {{Extraction of the intercellular skeleton from 2D images of embryogenesis using eikonal equation and advective subjective surface method}},
    author = {Bourgine, Paul and Frolkovic, Peter and Mikula, Karol and Peyrieras, Nadine and Remesikova, Mariana},
    abstract = {{We suggest an efficient method for automatic detection of the intercellular skeleton in microscope images of early embryogenesis. The method is based on the solution of two advective PDEs. First, we solve numerically the time relaxed eikonal equation in order to obtain the signed distance function to a given set - a set of points representing cell centers or a set of closed curves representing segmented inner borders of cells. The second step is a segmentation process driven by the advective version of subjective surface equation where the velocity field is given by the gradient of the computed distance function. The first equation is discretized by Rouy-Tourin scheme and we suggest a fixing strategy that significantly improves the speed of the computation. The second equation is solved using a classical upwind strategy. We present several test examples and we show a practical application - the intercellular.}},
    language = {English},
    affiliation = {Centre de recherche en {\'e}pist{\'e}mologie appliqu{\'e}e - CREA , R{\'e}seau National des Syst{\`e}mes Complexes - RNSC , Department of Mathematics - STUBA , Neurobiologie et D{\'e}veloppement - N\&eD , Institut des Syst{\`e}mes Complexes - Paris Ile-de-France - ISC-PIF , Institut de Neurobiologie Alfred Fessard - INAF},
    booktitle = {{Scale Space and Variational Methods in Computer Vision}},
    publisher = {Springer Verlag},
    pages = {38-49},
    editor = {Xue-Cheng Tai, Knut Morken, Marius Lysaker, Knut-Andreas Lie },
    series = {Lecture Notes in Computer Science volume 5567 },
    note = {2nd International Conference on Scale Space and Variational Methods in Computer Vision,Voss, NORWAY, JUN 01-05, 2009 },
    audience = {international },
    isbn = {9783642022555 },
    doi = {10.1007/978-3-642-02256-2\_4 },
    year = {2009},
}

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